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## NIMCET Previous Year Questions (PYQs)

#### NIMCET Permutations And Combinations PYQ

NIMCET PYQ
In a beauty contest, half the number of experts voted Mr. A and two thirds voted for Mr. B 10 voted for both and 6 did not for either. How may experts were there in all.

NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

#### Solution

Let the total number of experts be $N$.
$E$ is the set of experts who voted for miss $A$.
$F$ is the set of experts who voted for miss $B$.
Since $6$ did not vote for either, n$\left(E\cup F\right)=N-6$.
$n\left(E\right)=\frac{N}{2},\phantom{\rule{thickmathspace}{0ex}}n\left(F\right)=\frac{2}{3}N$ and $n\left(E\cap F\right)=10$
.
So, $N-6=\frac{N}{2}+\frac{2}{3}N-10$
Solving the above equation gives

NIMCET PYQ
If all the words, with or without meaning, are written using the letters of the word QUEEN add are arranged as in  English Dictionary, then the position of the word QUEEN is

NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

#### Solution

Letters of the word QUEEN are E,E,N,Q,U

Words beginning with E (4!) = 24

Words beginning with N (4!/2!)=12

Words beginning with QE (3!) =  6

Words beginning with QN (3!/2!)= 3

Total words = 24+12+6+9=45

QUEEN is the next word and has rank 46th.

NIMCET PYQ
In a chess tournament, n men and 2 women players participated. Each player plays 2 games against every other player. Also, the total number of games played by the men among themselves exceeded by 66 the number of games that the men played against the women. Then the total number of players in the tournament is

NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

#### Solution

NIMCET PYQ
If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is

NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

#### Solution

NIMCET PYQ
A polygon has 44 diagonals, the number of sides are

NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

#### Solution

NIMCET PYQ
9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging one ball in each of the boxes is

NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

#### Solution

First off all select 5 boxes out 6 boxes in which 5 big ball can fit then arrange these ball in these 5 boxes and then put remaining 4 ball in any remaining box.
So Ans is [(6C5)5!](4!) = 6!4! = 17280

NIMCET PYQ
A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and two Executive Committee members have to be elected. In how many ways this can be done?

NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

#### Solution

NIMCET PYQ
How many natural numbers smaller than  can be formed using the digits 1 and 2 only?

NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

#### Solution

NIMCET PYQ
If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is  minimum

NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

#### Solution

NIMCET PYQ
m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small cages and p large animal (n < p < m). The large animals are so large that they do not fit in small cage. However, small animals can be put in any cage. The number of putting the animals into cage is

NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

#### Solution

NIMCET PYQ
Let A and B two sets containing four and two elements respectively. The number of subsets of the A × B, each having at least three elements is

NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

#### Solution

n(A) = 4
n(B) = 2
Then the number of subsets in A*B is 2= 256

NIMCET PYQ
If , then the values of n and r are:

NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

#### Solution

NIMCET PYQ
There are 50 questions in a paper. Find the number of ways in which a student can attempt one or more questions :

NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

#### Solution

NIMCET PYQ
How many words can be formed starting with letter D taking all letters from the word DELHI so that the letters are not repeated:

NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

#### Solution

NIMCET PYQ
Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party?

NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

#### Solution

(10-3)C6= 7C6 = 7

NIMCET PYQ
There is a young boy’s birthday party in which 3 friends have attended. The mother has arranged 10 games where a prize is awarded for a winning game. The prizes are identical. If each of the 4 children receives at least one prize, then how many distributions of prizes are possible?

NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

#### Solution

NIMCET PYQ
In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is

NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

#### NIMCET

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